So, that’s simple enough, right? TimesPi stores a Real number $.x internally, and the value it represents is that number times pi. There’s a postfix operator π to make it really easy to construct these numbers. Because we’ve defined a Bridge method, this class has access to all the normal methods and operators of Real. Still, as presented above it is pretty useless, but defining some operators hints at a useful purposes for this class.

With these operators in place, basic arithmetic involving TimesPi numbers will stay in the TimesPi class when appropriate. For instance, if you add two TimesPi numbers, the result will be a TimesPi. The cool thing about this is that it is as exact $.x values allow, rather than forcing everything to be a floating point calculation of limited accuracy.

We can even take things a step further, using this to perform exact trig calculations: